Try and go on a Friday or Saturday when Tate doesn't close till 10pm. You won't feel rushed when trying to cover every exhibit in the massive building. Great views of the Thames as well!
Visit Vermeer's Girl with the Pearl Earring and step from side to side. You'll swear her vivid eyes are following you.
No music museum should be silent, yet this is the only instrument museum I know of that has recordings for most of the instruments readily accessible to visitors. Grab a pair of headphones and go!
Check on when the Mighty Wurlizter organ plays itself at appointed times!
Get 50% off admission (reg. $10). $5 tickets when you mention 8coupons.com (expires 8/20/11)
